As the title says, I want to have two tmux color schemes for day/night editing and I thought I could use $KONSOLE_PROFILE_NAME as a way to do this since I already set them up for konsole. But the variable is only set once when either a new tab or window starts and isn't updated otherwise.

I noticed that too, not sure if fixable because I don't see how Konsole could tell the shell to change that value, especially if an application is running (not at the command prompt), so cannot "inject" a command.

It only seem to work for new sessions.
The trick is simply to go to "New tab" then pick your profile name.